The Dispersion Equation of MGD Waves for non-stationary Plasmas

TL;DR

This paper derives a new dispersion equation for magnetogasdynamic (MGD) waves in non-stationary plasmas, accounting for relative motion and spatial gradients, revealing complex wave modes influenced by the plasma's reference frame speed.

Contribution

It introduces a generalized dispersion equation for MGD waves in moving plasmas, extending known stationary plasma models to include effects of relative motion and spatial gradients.

Findings

Derivation of a four-order dispersion equation for non-stationary plasmas.

Identification of Alfven and magnetogasdynamic wave modes affected by reference frame speed.

Reduction to known stationary plasma results when the reference frame speed is zero.

Abstract

The dispersion equation of MGD plasma waves measured in a reference frame with a relative speed from that where they are generated is derived. The analysis leads further from what is known for waves produced in stationary plasmas in the presence of an imposed magnetic field, and includes terms containing space gradients in the density and speed values in the continuity and momentum equations of the plasma. The dispersion equation that is derived leads to an Alfven wave and magnetogasdynamics wave modes whose distribution with respect the direction of the imposed magnetic field varies with the relative speed of the reference frame. For the particular case in which the speed of the reference frame is zero the dispersion equation of the magnetogasdynamic waves reduces to what is known for stationary plasmas. More complicated waves with different distribution modes with respect to the magnetic field direction are implied from the more general four-order dispersion equation that is derived. A particular case is presented for a non-zero speed value of the reference frame, but the derivation and analysis of the corresponding solutions will be discussed in a forthcoming report.